Rigid Body Reel and hanging mass.

[JJRKnights]

Homework Statement

An object with a mass of m = 5.4 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.265 m and mass of M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown in the figure below. The suspended object is released from rest 5.50 m above the floor.

(a) Determine the tension in the string.
(b) Determine the magnitude of the acceleration of the object.
(c) Determine the speed with which the object hits the floor.

Homework Equations

ƩFy = ma
τ = Iα

The Attempt at a Solution

ƩFy = mg - T = ma
T = m(g-a)
a = -10/t^2
I = .5(M)(R^2)
τ = Iα = .5MRa
τ=.3975a

I found that to find Tension in this way, I would need acceleration first, but there must be another way to find Tension because b) asks for acceleration while a) wants Tension.

Could I say that the Torque = Tension x Radius?

I think I'm on the right tracks, but can anybody help please?

 

[JJRKnights]

Also for part c,

I looked at it and can see relevant equations:

v^2 =(v_0)^2 + 2a(x-(x_0))
which would come out to
v^2 = -10a